Just got to the Watch.
Got level4 peacoat reward and equipped it.
Needed to go back to empty bags, they were ABOVE max level.
Couldn't use extract on garbage items to make space.
Clicked Travel to Respite, and while waiting I tried to apply an enchantment to my new peacoat.
Peacoat was then dropped!!!
Sent to respite before I could get it back in my bag because I was above the limit.
Went back to the Watch and peacoat was nowhere to be found.
Can I get my coat back?
I have a similar experience. I did not try traveling to respite yet (your post actually saved me from doing that).
I did, however, have a very full inventory. I wanted to try to do some minor cleanup, and so I tried to use up infusions. In doing so, I dropped my peacoat and my pistol. Since nothing can be extracted, eaten, or even willingly dropped - these items are sort of stuck until I reload the Watch, which will just delete them.
I was able to get someone from the Nightingale discord (Thanks Phylon!!!) to join my party and come grab the gear so it wouldn't be lost forever, but that's not going to be the experience for everyone unfortunately.